1. Field of the Invention (Technical Field)
The present invention relates to creation and use of long folded optical paths in a compact structure for use with lasers in making optical measurements or systems.
2. Description of Related Art
Note that the following discussion refers to a number of publications by author(s) and year of publication, and that due to recent publication dates certain publications are not to be considered as prior art vis-a-vis the present invention. Discussion of such publications herein is given for more complete background and is not to be construed as an admission that such publications are prior art for patentability determination purposes.
Multiple pass optical cells with dense spot patterns are very useful for many applications, especially when the cell volume must be minimized relative to the optical path length. Present methods to achieve these dense patterns require very expensive, highly precise astigmatic mirrors and complex alignment procedures to achieve the desired pattern. This invention describes a new, much simpler and less demanding mirror system that can meet all of the requirements and be easily aligned. It comprises of one inexpensive cylindrical mirror and one spherical mirror.
Multiple pass optical cells are used to achieve very long optical path lengths in a small volume and have been extensively used for absorption spectroscopy, (White, J. U., “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am., vol. 32, pp 285-288 (May 1942); Altmann, J. R. et al., “Two-mirror multipass absorption cell,” Appl. Opt., vol. 20, No. 6, pp 995-999 (15 Mar. 1981) laser delay lines (Herriott, D. R., et al., “Folded Optical Delay Lines,” Appl. Opt., vol. 4, No. 8, pp 883-889 (August 1965)), Raman gain cells (Trutna, W. R., et al., “Multiple-pass Raman gain cell,” Appl. Opt., vol. 19, No. 2, pp 301-312 (15 Jan. 1980)), interferometers (Herriott, D. H., et al., “Off-Axis Paths in Spherical Mirror Interferometers,” Appl. Opt., vol. 3, No. 4, pp 523-526 (April 1964)), photoacoustic spectroscopy (Sigrist M. W., et al., “Laser spectroscopic sensing of air pollutants,” Proc. SPIE, vol. 4063, pp. 17 (2000)) and other resonators (Yariv, A., “The Propagation of Rays and Spherical Waves,” from Introduction to Optical Electronics, Holt, Reinhart, and Winston, Inc., New York (1971), Chap. 2, pp 18-29; Salour, M. M., “Multipass optical cavities for laser spectroscopy,” Laser Focus, 50-55 (October 1977)).
These cells have taken the form of White cells (White, J. U., “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am., vol. 32, pp 285-288 (May 1942)) and its variants (Chernin, S. M. and Barskaya. E. G., “Optical multipass matrix systems,” Appl. Opt., vol. 30, No. 1, pp 51-58 (January 1991)), integrating spheres (Abdullin, R. M. et al., “Use of an integrating sphere as a multiple pass optical cell,” Sov. J. Opt. Technol., vol. 55, No. 3, pp 139-141 (March 1988)), and stable resonator cavities (Yariv, A., “The Propagation of Rays and Spherical Waves,” from Introduction to Optical Electronics, Holt, Reinhart, and Winston, Inc., New York (1971)).
The stable resonator is typified by the design of Herriott (Herriott, D. H., et al., “Off-Axis Paths in Spherical Mirror Interferometers,” Appl. Opt., vol. 3, No. 4, pp 523-526 (April 1964)). The simplest such Herriott cell consists of two spherical mirrors of equal focal lengths separated by a distance d less than or equal to four times the focal lengths f of the mirrors. This corresponds to stable resonator conditions. A collimated or focused laser beam is injected through the center of a hole in one of the mirrors, typically an off-axis location near the mirror edge. The beam is periodically reflected and refocused between these mirrors and then exits through the center of the input hole (corresponding exactly to the entry position of the input beam, defining the re-entrant condition) after a designated number of passes N, in a direction (slope) that is different from the entry slope. As a result, the total optical path traversed in the cell is approximately N×d. The pattern of reflected spots observed on the mirrors in these cells forms an ellipse. Re-entrant conditions for spherical mirror Herriott cells are restricted by certain predetermined ratios of the mirror separation d to the focal length f and the location and slope of the input beam. For any re-entrant number of passes N, all allowed solutions are characterized by a single integer M. Excellent descriptions for the design, setup and use of these cells are given by Altmann (Altmann, J. R., et al., “Two-mirror multipass absorption cell,” Appl. Opt., vol. 20, No. 6, pp 995-999 (15 Mar. 1981) and McManus (McManus, J. B., et al., “Narrow optical interference fringes for certain setup conditions in multipass absorption cells of the Herriott type,” Appl. Opt., vol. 29, No. 7, pp 898-900 (1 Mar. 1990)).
When the cell volume must be minimized relative to the optical path length or where a very long optical path (>50 m) or very small footprint is desired, it is useful to increase the density of passes per unit volume of cell. The conventional spherical mirror Herriott cell is limited by the number of spots one can fit along the path of the ellipse without the spot adjacent to the output hole being clipped by or exiting that hole at a pass number less than N. This approximately restricts the total number of passes to the circumference of the ellipse divided by the hole diameter, which in turn is limited by the laser beam diameter. For a 25-mm radius mirror with a relatively small 3-mm diameter input hole located 20 mm from the center of the mirror, a maximum of about (2×π×20)/3=40 spots, or 80 passes is possible at best. Generally the hole is made larger to prevent any clipping of the laser input beam that might lead to undesirable interference fringes, and typical spherical Herriott cells employ less than 60 passes.
Herriott (Herriott, D. R. and Schulte, H. J., “Folded Optical Delay Lines,” Appl. Opt., vol. 4, No. 8, pp 883-889 (Aug. 1965)) demonstrated that the use of a pair of astigmatic mirrors could greatly increase the spot density, and hence optical path length, in the cell. Each mirror has different finite focal lengths (fx and fy) along orthogonal x and y axes, and the mirrors are aligned with the same focal lengths parallel to one another. The resulting spots of each reflection on the mirrors create precessions of ellipses to form Lissajous patterns. Since these patterns are distributed about the entire face of each mirror, many more spots can be accommodated as compared to a cell with spherical mirrors. Herriott defines the method of creating the astigmatic mirror as distortion of a spherical mirror, either in manufacture or in use, by squeezing a spherical mirror in its mount. He states that the amount of astigmatism required is very small and amounts to only a few wavelengths. McManus (McManus, et al., “Astigmatic mirror multipass absorption cells for Ion-path-length spectroscopy,” Appl. Opt., vol. 34, No. 18, pp 3336-3348 (20 Jun. 1995)) outlines the theory and behavior of this astigmatic Herriott cell and shows that the density of passes can be increased by factors of three or more over spherical mirror cells. For these astigmatic mirror cells, light is injected through a hole in the center of the input mirror. Allowed solutions for re-entrant configurations are characterized by a pair of integer indices Mx and My, since there are now two focal lengths present along orthogonal axes.
The drawback of this design is that the constraints to achieve useful operation are very severe. First of all, both Mx and My must simultaneously be re-entrant, so that for a desired N and variable distance d, the focal lengths fx and fy, must be specified to a tolerance of 1 part in 104. Since mirrors can rarely be manufactured to such tolerances, this cell as originally proposed is impractical for routine use. However, Kebabian (U.S. Pat. No. 5,291,265 (1994)) devised a method to make the astigmatic cell usable. Starting with the astigmatic Herriott setup with the same mirror axes aligned, he then rotates one mirror relative to the other around the z-axis (FIG. 2), thereby mixing the (previously independent) x and y components of the beam co-ordinates. A moderate rotation of ˜5-20 degrees and a small compensating adjustment of the mirror separation distance can accommodate the imprecision in the manufacturing of the mirror focal lengths. However, this approach is still difficult to achieve in practice and requires complex calculations and skill to get to the desired pattern. Furthermore, the astigmatic mirrors must still be custom made and cost many thousands of dollars for a single pair.
Recently, Hao (Hao, L.-Y., et. al., “Cylindrical mirror multipass Lissajous system for laser photoacoustic spectroscopy,” Rev. Sci. Instrum., vol. 73, No. 5, pp. 2079-2085 (May 2002)) described another way to generate dense Lissajous patterns using a pair of cylindrical mirrors, each having a different focal length, and where the principal axes of the mirrors are always orthogonal to one another. In essence, this creates a pair of mirrors whose x-axis contains one curved surface (on mirror A) of focal length fx and one flat mirror surface (on mirror B), and in the y-axis contains one flat mirror surface (on mirror A) and one curved surface of focal length fy (on mirror B), where fx≠fy. Formulas to predict the spot patterns on each mirror are provided. The advantage to this system is that the dense Lissajous patterns can be formed from a pair of inexpensive mirrors, in contrast to the requirement for custom astigmatic mirrors (we note that for a practical commercial multipass cell, one cannot rely on simply squeezing spherical mirrors to achieve a reliable long term, stable set of focal lengths. Thus diamond turned custom astigmatic mirrors must be made). The drawback of this mismatched focal length pair of cylindrical mirrors is that, similar to the astigmatic Herriott cell, for a given pair of focal lengths, there is only one allowed re-entrant solution value of N permitted. Of course, for photoacoustic measurements as intended by Hao, where any exiting light is not detected, the light does not necessarily have to be re-entrant and many values of mirror separation which are not re-entrant, but do generate many passes, are useful.
Silver, in U.S. patent application Ser. No. 10/896,608, parent to the present application, recently introduced a method for achieving dense patterns using a pair of nominally matched cylindrical mirrors whereby the desired patterns can readily and reliably be set using inexpensive mirrors. A key feature of this system is that nearly any reasonable number of passes can be achieved using a single set of mirrors, in contrast to the orthogonal mismatched cylindrical pair of Hao or the astigmatic mirrors of Kebabian. The desired number of passes and overall optical path are set by rotating the cylindrical axes relative to one another at a predetermined mirror separation.
The present invention describes a very simple, low cost, high density, multipass optical cell, where no rotation of the mirrors is needed (in fact, with a spherical-cylindrical mirror pair, no rotation axis can be defined because the spherical mirror is fully symmetric). The key to this invention is to use near, but not exact re-entrant conditions as are common to all of the above-referenced methods. Contrary to the teachings of all multipass mirror papers and patents, exact re-entry is not a necessary criterion for practical use, but does simplify use in most cases. However, with the spherical-cylindrical mirror pair, there are very few or no exact re-entrant solutions (depending on the focal lengths of the mirrors) but only a limited, but useful, number of nearly re-entrant solutions exist. Thus it becomes a relatively easy task to identify good near re-entrant solutions and to align any given mirror system to achieve these solutions. As long as this mirror system is a stable resonator, then the desired number of passes can be achieved simply by setting d to the predicted value based on the mirror focal lengths. When the laser beam enters through the center of one mirror, a dense pattern of spots forms and the position of the beam as it exits this hole is readily predicted.
Unlike all other dense cell methods, this invention relies neither on the absolute manufactured focal lengths or mirror twist angles, but only on the relative mirror separation ratio d/f.